On Iso-Dual MDS Codes From Elliptic Curves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916595760103424 |
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| author | Zhu, Yunlong Zhao, Chang-An |
| author_facet | Zhu, Yunlong Zhao, Chang-An |
| contents | For a linear code $C$ over a finite field, if its dual code $C^{\perp}$ is equivalent to itself, then the code $C$ is said to be {\it isometry-dual}. In this paper, we first confirm a conjecture about the isometry-dual MDS elliptic codes proposed by Han and Ren. Subsequently, two constructions of isometry-dual maximum distance separable (MDS) codes from elliptic curves are presented. The new code length $n$ satisfies $n\le\frac{q+\lfloor2\sqrt{q}\rfloor-1}{2}$ when $q$ is even and $n\le\frac{q+\lfloor2\sqrt{q}\rfloor-3}{2}$ when $q$ is odd. Additionally, we consider the hull dimension of both constructions. In the case of finite fields with even characteristics, an isometry-dual MDS code is equivalent to a self-dual MDS code and a linear complementary dual MDS code. Finally, we apply our results to entanglement-assisted quantum error correcting codes (EAQECCs) and obtain two new families of MDS EAQECCs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Iso-Dual MDS Codes From Elliptic Curves Zhu, Yunlong Zhao, Chang-An Information Theory For a linear code $C$ over a finite field, if its dual code $C^{\perp}$ is equivalent to itself, then the code $C$ is said to be {\it isometry-dual}. In this paper, we first confirm a conjecture about the isometry-dual MDS elliptic codes proposed by Han and Ren. Subsequently, two constructions of isometry-dual maximum distance separable (MDS) codes from elliptic curves are presented. The new code length $n$ satisfies $n\le\frac{q+\lfloor2\sqrt{q}\rfloor-1}{2}$ when $q$ is even and $n\le\frac{q+\lfloor2\sqrt{q}\rfloor-3}{2}$ when $q$ is odd. Additionally, we consider the hull dimension of both constructions. In the case of finite fields with even characteristics, an isometry-dual MDS code is equivalent to a self-dual MDS code and a linear complementary dual MDS code. Finally, we apply our results to entanglement-assisted quantum error correcting codes (EAQECCs) and obtain two new families of MDS EAQECCs. |
| title | On Iso-Dual MDS Codes From Elliptic Curves |
| topic | Information Theory |
| url | https://arxiv.org/abs/2502.02033 |